论文标题
Schatten和Sobolev对紧凑的海森堡歧管的绿色操作员的估计
Schatten and Sobolev Estimates for Green Operators on Compact Heisenberg Manifolds
论文作者
论文摘要
令$ m =γ\ setMinus \ mathbb {h} _d $是$ d $ d $ d $ d $ diperional heisenberg $ \ mathbb {h} _d $的紧凑商。我们为绿色操作员$ \ MATHCAL {G}_α$与二阶差速器家族的固定元素相关的绿色操作员$ \ weft \ left \ left \ {l}_α_α\ right \} $相关的Schatten和Sobolev估计。特别是，因此，$ m $上的功能上的科恩·拉普拉斯（Kohn Laplacian）是次要的。我们的主要工具是Folland对$ \ Mathcal {l}_α$的频谱的描述。
Let $M = Γ\setminus \mathbb{H}_d$ be a compact quotient of the $d$-dimensional Heisenberg group $\mathbb{H}_d$ by a lattice subgroup $Γ$. We give Schatten and Sobolev estimates for the Green operator $\mathcal{G}_α$ associated to a fixed element of a family of second order differential operators $\left\{ \mathcal{L}_α\right\}$ on $M$. In particular, it follows that the Kohn Laplacian on functions on $M$ is subelliptic. Our main tool is Folland's description of the spectrum of $\mathcal{L}_α$.
